Graded HyperRough Set and Linguistic HyperRough Set

Takaaki Fujita , Arif Mehmood

Numerous mathematical frameworks have been developed to handle uncertainty, including Fuzzy Sets,1 Intuitionistic Fuzzy Sets,2 Hyperfuzzy Sets,3 Picture Fuzzy Sets,4 Hesitant Fuzzy Sets,5, 6 Neutrosophic Sets,7 Plithogenic Sets,8 and Soft Sets,9 and research in this area continues to evolve rapidly. Rough set theory provides a foundational method for approximating subsets using lower and upper bounds based on equivalence relations, offering an effective approach to modeling uncertainty in classification and data analysis.10, 11 Building upon these foundations, extended models such as HyperRough Sets and SuperHyperRough Sets have been proposed.12 In this paper, we present novel definitions that further generalize Graded Rough Sets and Linguistic Rough Sets—specifically, the Graded HyperRough Set and the Linguistic HyperRough Set. These new frameworks are expected to contribute to the advancement of research in fields such as decision-making, language theory, and artificial intelligence.

Doi: https://doi.org/10.54216/GJMSA.120201

Vol. 12 Issue. 2 PP. 01-23, (2025)